Question

At constant volume, a container of gas at 1 atm is heated from 300K to 350K. What is the final pressure?

a
0.35 atm
b
0.86 atm
c
1.2 atm
d
2.8 atm

Answer 1

To find the final pressure of a gas when it is heated at constant volume, you can use the ideal gas law, which in terms of pressure and temperature can be expressed as:

\[
\frac{P_1}{T_1} = \frac{P_2}{T_2}
\]

Where:
- \( P_1 \) is the initial pressure
- \( T_1 \) is the initial temperature
- \( P_2 \) is the final pressure
- \( T_2 \) is the final temperature

In this case, you have:
- \( P_1 = 1 \, \text{atm} \)
- \( T_1 = 300 \, \text{K} \)
- \( T_2 = 350 \, \text{K} \)

Now, rearrange the equation to solve for \( P_2 \):

\[
P_2 = P_1 \times \frac{T_2}{T_1}
\]

Substituting the values in:

\[
P_2 = 1 \, \text{atm} \times \frac{350 \, \text{K}}{300 \, \text{K}} = 1 \, \text{atm} \times 1.1667 \approx 1.1667 \, \text{atm}
\]

This is approximately equal to 1.17 atm.

Since this value is closest to option (c) 1.2 atm, the correct answer is:

**c. 1.2 atm**